Question

A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by ℎ() = −4.9² + 229 + 234. What is the significance of the coefficient -4.9 in the equation?

Answer 1

The coefficient -4.9 in the rocket's height equation represents the acceleration due to gravity, which affects the rocket's vertical motion by decreasing its upward velocity at a constant rate.

Step-by-step explanation:

The coefficient -4.9 in the equation for a rocket's height as a function of time, h(t) = -4.9t² + 229t + 234, refers to the acceleration due to gravity in meters per second squared, with a negative sign indicating that gravity is a downward force acting against the upward motion of the rocket. This coefficient is part of the kinematic equation that describes the vertical motion under constant acceleration.

In the context of projectile motion, the significance of this coefficient is that it represents the constant rate at which the rocket's upward velocity is decreasing due to gravity, ultimately determining the time the projectile spends in the air and its maximum height. When a projectile is launched upwards, gravity slows it down until it momentarily comes to a stop at its peak height before descending back down.